Modus Tollens(Note: You will need Internet Explorer 6.0.2x or greater to view the mathematical symbols in this page correctly)
In sentential logic (also known as propositional calculus or sentential
calculus) the representation of modus tollens is:
(P→Q)∧¬Q→ ¬P
where
→ is the symbol for logical implication and
∧ is the symbol for logical conjunction.
¬ is the symbol for negation
Replacing symbolic logical operators with word equivalents, this reads as:
if P implies Q and not Q, then not P
where P and Q are both sentences incorporating assertions.
The predicates (including the conditional statement and the negated consequent) and the antecedent are frequently laid out line by line and enumerated.
1. P→Q
2. ¬Q
————
3. ¬P
Example.
Let P be the sentence 'If it is raining' and Q be the sentence 'There will be clouds overhead'. Then modus tollens will involve the two sentences in conjunction and the negation of the second sentence (Q) as the predicates, with the negation of sentence P as the result.
'If it is raining, there will be clouds overhead'
'There are no clouds overhead'
—————————————————
'It is not raining'
Editor(s): Long, B.
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